Hydraulic actuators in many machines are subjected to varying loads. The loads may be overrunning loads or resistive loads. An overrunning load is a load that acts in the same direction as the motion of the actuator. Examples of overrunning loads include lowering a wheel loader boom or lowering an excavator boom, each with gravity assistance. A resistive load is a load that acts in the opposite direction as the motion of the actuator. Examples of resistive loads include raising a wheel loader boom or raising an excavator boom, each against the force of gravity. In certain applications, hydraulic actuators can be subjected to both an overrunning load and a resistive load in the same extend or retract stroke. As an example, when a wheel loader bucket that is curled in is given a command to curl out (generally, a retraction of the actuator), the motion may begin with a resistive load applied to the actuator and, at some point in the stroke, typically due to the force of gravity, the load on the actuator becomes an overrunning load. The transition between the resistive load and the overrunning load without a change in the direction of motion is referred to herein as an “over-center load condition.” An over-center load condition may occur during a transition from a resistive load to an overrunning load and during a transition from an overrunning load to a resistive load.
It is desirable that an over-center load condition not affect the velocity of retraction or extension of the actuator. Such velocity control is particularly difficult when the hydraulic actuator is an unbalanced actuator of an electro-hydraulic actuation (EHA) system. An unbalanced actuator has unequal cross-sectional areas on opposite sides of the piston, generally as a result of the rod being attached to only one side of the piston. An EHA system is a system in which a reversible, variable speed electric motor is connected to a hydraulic pump, generally fixed displacement, for providing fluid to an actuator for controlling motion of the actuator.